Finally use [[tau].sub.0] to calculate the

instantaneous frequency to(t), and get the fundamental frequency F0 by (23), (24), and (25):

Figure 6 shows the tracked IMF (IMF 3) of interest whose

instantaneous frequency (IF) oscillates around 0.5 Hz.

(3) enables us to represent the amplitude and the

instantaneous frequency as functions of time in a threedimensional space.

where [a.sub.i](t) and [f.sub.i](t) represent the instantaneous amplitude and

instantaneous frequency, respectively, and N is the number of PF component.

Giakas, "Fatigue analysis of the surface EMG signal in isometric constant force contractions using the averaged

instantaneous frequency," IEEE Transactions on Biomedical Engineering, vol.

The

instantaneous frequency amplitude of MFSK signals after wavelet transform can be approximated as followed:

Step 2: Use LMD method to decompose the purified signal into PFs, meantime instantaneous amplitude and

instantaneous frequency of each PF component can be calculated.

For each [k.sup.th] IMF was calculated its Hilbert transform [H.sub.k][n] and the

instantaneous frequency:

The strong analytic signal can be written with the amplitude and the phase where the derivative of the phase can be identified as the

instantaneous frequency. The Hilbert transform defined in the time domain is a convolution between the Hilbert transformer 1/[pi]t and the real function x(t):

The

instantaneous frequency (IF) can be gotten by w(t) - d[theta](t)/d(t).

The

instantaneous frequency of each IMF will be derived by the Hilbert-Huang transform, and then the Hilbert spectrum will be obtained by integrating all the

instantaneous frequency spectrums.

Based on most SAR echoes with RFI, the interference takes on spikes in the

instantaneous frequency spectrum [7].